Topology at the deconfinement transition uncovered by inverse blocking in SU(2) pure gauge theory with fixed point action

Feurstein, Markus; Ilgenfritz, E. M.; Müller–Preussker, M.; Thurner, S.

doi:10.1016/s0550-3213(97)00738-4

Cited by 19 publications

(31 citation statements)

References 59 publications

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“…Traditionally, the presence of locally classical excitations like instantons in Monte Carlo lattice gauge fields has been explored by using methods like cooling [26,27,28,29], restricted cooling [30], smearing [31], that replaced the more demanding RG cycling [32,33], and more general, by combinations of blocking and inverse blocking [34,35,36]. In the result, a well-localized topological charge density (according to its field-theoretical definition [37,38]) becomes visible.…”

Section: Introductionmentioning

confidence: 99%

Calorons and dyons at the thermal phase transition analyzed by overlap fermions

et al. 2007

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In a pilot study, we use the topological charge density defined by the eigenmodes of the overlap Dirac operator (with ultraviolet filtering by mode-truncation) to search for lumps of topological charge in SU (2) pure gauge theory. Augmenting this search with periodic and antiperiodic temporal boundary conditions for the overlap fermions, we demonstrate that the lumps can be classified either as calorons or as separate caloron constituents (dyons). Inside the topological charge clusters the (smeared) Polyakov loop is found to show the typical profile characteristic for calorons and dyons. This investigation, motivated by recent caloron/dyon model studies, is performed at the deconfinement phase transition for SU (2) gluodynamics on 20 3 × 6 lattices described by the tadpole improved Lüscher-Weisz action. The transition point has been carefully located. As a necessary condition for the caloron/dyon detection capability, we check that the LW action, in contrast to the Wilson action, generates lattice ensembles, for which the overlap Dirac eigenvalue spectrum smoothly behaves under smearing and under the change of the boundary conditions.

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Section: Introductionmentioning

confidence: 99%

Calorons and dyons at the thermal phase transition analyzed by overlap fermions

et al. 2007

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“…It has been objected that these methods modify the field configurations in an uncontrolled way such that the observed excitations could actually be fake and do not represent the relevant nonperturbative fields. Other smoothing techniques also reveal lumps of action which are usually interpreted as instantons [1,2]. In order to relate these structures to confinement, some additional degrees of freedom seemed to be necessary.…”

Section: Introductionmentioning

confidence: 99%

Laplacian modes probing gauge fields

Bruckmann

Ilgenfritz

2005

Phys. Rev. D

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We show that low-lying eigenmodes of the Laplace operator are suitable to represent properties of the underlying SU (2) lattice configurations. We study this for the case of finite temperature background fields, yet in the confinement phase. For calorons as classical solutions put on the lattice, the lowest mode localizes one of the constituent monopoles by a maximum and the other one by a minimum, respectively. We introduce adjustable phase boundary conditions in the time direction, under which the role of the monopoles in the mode localization is interchanged. Similar hopping phenomena are observed for thermalized configurations. We also investigate periodic and antiperiodic modes of the adjoint Laplacian for comparison.In the second part we introduce a new Fourier-like low-pass filter method. It provides link variables by truncating a sum involving the Laplacian eigenmodes. The filter not only reproduces classical structures, but also preserves the confining potential for thermalized ensembles. We give a first characterization of the structures emerging from this procedure.

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“…This evidence stems from the observation made for one-instanton and manyinstanton configurations [19,20] in the maximally Abelian gauge and from the observation of short range correlations between topological charge and magnetic currents in genuine confining lattice configurations [21,22]. On the other hand, also in artificial instanton liquid model ensembles (multi(anti)instanton configurations) monopole network percolation has been observed [23] as a prerequisite of monopole condensation.…”

Section: Introductionmentioning

confidence: 89%

Topological content ofSU(2)gauge fields belowTc

et al. 2002

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Finite temperature Euclidean SU (2) lattice gauge fields generated in the confinement phase close to the deconfinement phase transition are subjected to cooling. The aim is to identify long-living, almost-classical local excitations which carry (generically non-integer) topological charge. Two kinds of spatial boundary conditions (fixed holonomy and standard periodic boundary conditions) are applied. For the lowest-action almost-classical configurations we find that their relative probability semi-quantitatively agrees for both types of boundary conditions. We find calorons with unit topological charge as well as (anti-)selfdual lumps (BPS-monopoles or dyons) combined in pairs of non-integer (equal or opposite sign) topological charge. For calorons and separated pairs of equal-sign dyons obtained by cooling we have found that (i) the gluon field is well-described by Kraan-van Baal solutions of the Euclidean Yang-Mills field equations and (ii) the lowest Wilsonfermion modes are well-described by analytic solutions of the corresponding Dirac equation. For metastable configurations found at higher action, the multi-center structure can be interpreted in terms of dyons and antidyons, using the gluonic and fermionic indicators as in the dyon-pair case. Additionally, the Abelian monopole structure and field strength correlators between the centers are useful to analyse the configurations in terms of dyonic constituents. We argue that a semi-classical approximation of the non-zero temperature path integral should be built on superpositions of solutions with non-trivial holonomy.

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Topology at the deconfinement transition uncovered by inverse blocking in SU(2) pure gauge theory with fixed point action

Cited by 19 publications

References 59 publications

Calorons and dyons at the thermal phase transition analyzed by overlap fermions

Calorons and dyons at the thermal phase transition analyzed by overlap fermions

Laplacian modes probing gauge fields

Topological content ofSU(2)gauge fields belowTc

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